Rewrite as a simplified fraction. ${0.9\overline{86} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 986.8686...\\ 10x &= 9.8686...\end{align*}}$ Subtracting the two equations, we have: ${990x = 977}$ ${x = \dfrac{977}{990}} $